1. Field of the Invention
The present invention relates to a method for generating a three-dimensional image of a ground area using a radar with a synthetic aperture, a SAR radar. Important applications are, inter alia,
three-dimensional positioning of the ground surface and/or objects close to the ground surface,
topographic mapping where no ground check points are available, and
topographic mapping of various ground layers, especially underlying ground surface in wooded areas.
2. Description of the Related Art
SAR is an established technique for two-dimensional ground mapping with a high resolutions in this technique, short radar pulse are transmitted, or longer pulses which am compressed using a pulse compression technique, from a platform, e.g. aircraft or satellite, moving along a nominal straight path over the area of ground that is to be studied, and the change of the return signal during the movement of the platform is analysed.
The short pulse allows a high range resolution, transversely of the straight path, while a linear combination of the signals along the straight path results in a high azimuth resolution, along the straight path. The latter is equivalent to an extended antenna aperture, which is synthesised by signal processing. The condition for achieving a high azimuth resolution is that the relative amplitude and phase of the transmitted and received radar pulse are known, and that the position of the antenna is measured with great accuracy along the aperture.
The SAR technique has in realised over a wide frequency band, between about 20 MHz and 100 GHz, which corresponds to electromagnetic wavelengths between 3 mm and 15 m. Since the interaction of the reflecting structures with the electro-magnetic wave is wavelength-dependent the imaging of various surface structures differs to a considerable extent according to the frequency at which they are illuminated.
As a rule, the penetration of the wave and also the size of the dominating scattering elements decrease for higher frequencies, both being of wavelength order. For woods, for instance, this means that it is fundamentally transparent for low frequencies ( less than 100 MHz) while high frequencies ( greater than 10 GHz) image the tree tops. By a suitable selection of frequency, it is thus possible to image layers on different levels in vegetation. Layers below th ground surface can be reproduced in similar ways. Polarisation and angle of incidence also affect the penetration of the wave and the scattering elements, even if this dependence is normally subordinated to the wavelength dependence.
Each point in the grid of the SAR image corresponds to a two-dimensional position defined by the transverse distance to a ground object and its position along the path. The position thus is unambiguous if the topography of the ground surface is known except for its mirror image through the flight path. The latter, however, can be distinguished by using the directivity of the antenna system.
The position of the ground is thus obtained as the intersection between a circular cylinder with the flight path as symmetry axis, the range cylinder, and two surfaces, one of which is a semiplane perpendicular to the cylinder axis, the azimuth plane, and the other represents the ground surface, see FIG. 1. This fact also means that the topography must be known a priori if the SAR image is to be registered to a map projection, which in most cases is a requirement made by those who are going to use the images in practice.
If, on the other hand, the topography of the ground surface is not known, the two-dimensional geometry of the SAR image means that ground structures with the same range and azimuth co-ordinates cannot possibly be distinguished from each other. It would thus be great progress of the SAR technique could be improved such that also the topography of the ground surface could be unambiguously determined on the basis of the SAR signal.
Narrow band SAR interferometry and stereo SAR are prior-art techniques for approximately determining the topography of the ground. Here a combination is made of measurements from two parallel-displaced paths, which is illustrated in FIG. 2. These techniques are based on the use of narrow band SAR systems which in the interferometry case result in ambiguity and in the stereo case result in insufficient height resolution. They are both based on the principle that the difference in range between two surface structures differs in the two images owing to the change in measurement geometry which is related to a difference in height. By using narrow band SAR, there will, however, be speckle noise in the image owing to the fact that the geometric resolution is much greater than the electromagnetic wavelength.
In these cases, the resolution volume generally contains multiple scattering elements which each backscatter the incident wave, which are superposed with amplitude and phase in the reconstructed image element. Superposition is equal to interference between to backscattered waves, and the resulting ground reflex thus is dependent on the angle of observation of the radar relative to the resolution volume.
In narrow band SAR where the resolution is much greater than the wavelength, the interference pattern changes very rapidly when the direction of observation changes. If, on the other hand, the resolution is of wavelength size, such as in broadband SAR, the direction of observation can change considerably without significantly affecting the interference pattern.
Normally the resolution volume contains many independent scattering elements, which results in random amplitude and phase between different resolution cells, so-called speckle noise. The interference pattern is reproducible if exactly the same measurement geometry is repeated, but it changes if the angle of observation or the character of the ground changes. The angle through which the interference pattern is correlated in inverse proportion to the extent of the resolution volume and is in proportion to half the wavelength, which is illustrated in FIG. 3.
Narrow band SAR interferometry uses the fact that the speckle noise is correlated when the change in measurement geometry is small. In this way, changes in the difference in range are determined with an accuracy which is a fraction of a wavelength. It is disadvantageous, however, that the measurement of the difference in range is ambiguous with a multiple of half the wavelength. If the maximum acceptable change in measurement geometry with retained correlation is taken into consideration, defined as a change in range difference between neighbouring resolution cells which is smaller than half the wavelength, the height resolution is of the same order as the range resolution. In practice, this means a vertical error in the order of 1-10 m for the currently most advanced narrow band SAR systems. A drawback of the method, however, is the ambiguity which must be solved by using special algorithms, xe2x80x9cphase unwrappingxe2x80x9d. A further drawback is that a measurement error of wavelength size, for instance an extra delay in the atmosphere, results in a great vertical error. To determine an unambiguous topographic height manual corrections therefore are necessary.
Narrow band stereo SAR uses the fact that certain structures can be recognised in the amplitude images. However, the speckle pattern is not correlated in the two images, which means that only relatively large structures can be measured. By amplitude correlation over the image, the distances to the structure in the two images are thus determined, which is converted to a height. Stereo SAR is disadvantageous above all by the speckle noise in the two images being uncorrelated, which results in the range difference being only determinable with an error which is considerably greater than the range resolution. In practice, this means that the vertical error is in the order of 10-100 m. A further drawback of the stereo technique is that it is based on the recognition of noisy structures in two images, which requires robust pattern recognition algorithms.
In view of the foregoing, a need exists to improve the SAR technique such that the topography of the ground surface could be determined on the basis of the SAR signal in an unambiguous manner and with great accuracy. The objective of the present invention is to solve this problem, which is achieved through a method for generating a three-dimensional image of a ground area using a synthetic aperture radar (SAR) supported by a platform moving in an essentially rectilinear manner. The method includes the steps of advancing the platform such that at least two images of the ground are created with a large difference in the angle of illumination, and transmitting radar pulses with a fractional bandwidth which is larger than or equal to 0.1, using in the computations an aperture angle which is larger than or equal to 0.1 radians. The method continues by detecting the reflected radar pulses with amplitude and phase and, for each pulse, measuring and storing the position of the antenna transmitting and the antenna receiving the pulse. A two-dimensional SAR signal per synthetic aperture is computed and, starting from the amplitude and phase of the SAR signals as well as position data for the antennae, the method proceeds by reconstructing a three-dimensional position description, topography, of the area relative to antenna position data, the topography being inverted from the measured SAR signals starting from a geometric signal model with the topography of the area and the position data of the antennae as input parameters, using the fact that the amplitude of the signals gives a topography with a coarse resolution but with a limited depth of focusing, which together with the phase of the signals gives an unambiguous topography with a fine resolution.
The method of the present invention may further include advancing the platform such that at least two images of the ground are created with a great difference in the angle of incidence, which takes place from antenna positions that differ by a distance perpendicular to the platform path by the platform moving in time successively along two essentially parallel-displaced paths. The platform may also be advanced such that at least two images of the ground are created with a great difference in the angle of incidence, which takes place from antenna positions that differ by a distance perpendicular to the platform path by transmitting simultaneously or alternatingly radar signals from two antennae on the platform.
Further embodiments include back-projecting the SAR signals to a three-dimensional computational grid along circles defined by the intersection between range cylinders and azimuth planes for each straight path, i.e. for each grid point, a value is set that is given by interpolation of the SAR signals to the range and azimuth positions of the given point. The method may be further characterized by maximizing, with a view to determining the vertical position in each horizontal position, in these horizontal positions the cross-correlation of the amplitude of the back-projected SAR signals in respect to the vertical position. A more accurate vertical position may also be determined in each horizontal position by determining in each horizontal position the vertical position for which the back-projected SAR signals have the same phase value and which is closest to the previously determined vertical position.
Additional embodiments include filtering the SAR signals starting from the local inclination and the SAR measuring geometry such that the ground-projected resolution elements become identical. The method may be carried out at least at two center frequencies, which gives the position of different vegetation layers and/or ground layers. Radar pulses may be transmitted and received at least at one higher center frequency, with the transmission taking place with a normal bandwidth.